The Number System With Base 36

As we already know, the number of digits in any base (radix) N
is exactly the same number N. For example, in the binary (N = 2) system there are two digits: 0 and 1; in the decimal (N = 10) there are ten of them: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. What if N exceeds 10?

If N > 10, the missing digits come from the alphabet (usually disregarding the case.) Thus A stands for the decimal 10 in any number system with base greater than 10. B stands for the decimal 11 in any number system with base greater than 11, and so on. The counter on the Content and Front pages cycles through representations of the same number in bases from 2 through 20. In base 20, we have the following 20 digits:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, G, H, I, J.

This is enough to occasionally get meaningful words. For example, FACE, BEEF, CAFE, DEED, BAD, CAD, FADE may appear even in the hexadecimal (N = 16) system. For a larger radix there are more examples: HIGH, FIG, JADE, JIBE, DIG.

The ultimate inclusion of the alphabet comes with the base 36 where we need 36 digits. In base 36, every single English word represents a number. So it becomes less of a fun to seek numbers represented by a meaningful combination of letters. We become more selective. We may look not for just any word but for words representing numbers with some special properties.